# Full text of "Analytical Mechanics"

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```FIELDS OF FORCE AND NEWTONIAN POTENTIAL    20^
Splitting equation (I) into three component equations wi have
X=-— /
dX '
7 = -^
Equations (I) and (I7) state that the force along a given direc tion which a particle experiences by virtue of its potential energy equals the rate of diminution of the potential energy along th given direction.
172. Torque Experienced by a Rigid Body in a Field of Force — Suppose the rigid body to be displaced under the action o the forces of the field through an angle dB. Then an amoun of work G dd is done, where G is the torque which the bod^ experiences in the field. By the principles of the conserva tion and degradation of dynamical energy this work mus come from the potential energy of the body in the field Therefore denoting the rate of increase in the potential energ;
of the body, due to a rotation about a given axis, by — w
66
have
n           dU                                                  fTT
<?=--•                                         (II
Equation (II) states that the torque which a rigid body experi ences by virtue of its potential energy equals the rate of diminu tion of this energy as the body turns about the axis of th torque.
order to overcome the forces which the particle experiences because of its pc sition in a field of force, and thereby to bring the particle from the etandar configuration to the one in which it has potential energy U.```